Detect / Remove a keylogger?

I received an email that went straight to spam indicating the sender had installed a keylogger on my computer and copied all my contacts, etc. etc. My concern is, they do actually have one of my passwords (for one or possibly 2 accounts) which they typed into the email threat. Can I just change my password from a different computer or how can I detect whether a keylogger was installed? What steps should I take next to ensure I don't get hacked, etc.?

Thanks!